Calculate the fraction of the group.

: $\frac{1}{2}$ of 6

Step 1: Calculate the fraction of the group.

$$\frac{1}{2} \times 6 = \frac{6}{2} = 3$$

The completed number sentence is $\frac{1}{2}$ of $6 = \boxed{\textbf{3}}$.

: $\frac{1}{2}$ of 8

Step 1: Calculate the fraction of the group.

$$\frac{1}{2} \times 8 = \frac{8}{2} = 4$$

The completed number sentence is $\frac{1}{2}$ of $8 = \boxed{\textbf{4}}$.

: $\frac{1}{2}$ of 12

Step 1: Calculate the fraction of the group.

$$\frac{1}{2} \times 12 = \frac{12}{2} = 6$$

The completed number sentence is $\frac{1}{2}$ of $12 = \boxed{\textbf{6}}$.

: $\frac{2}{3}$ of 6

Step 1: Calculate the fraction of the group.

$$\frac{2}{3} \times 6 = \frac{12}{3} = 4$$

The completed number sentence is $\frac{2}{3}$ of $6 = \boxed{\textbf{4}}$.

: $\frac{3}{4}$ of 8

Step 1: Calculate the fraction of the group.

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